Notice that the adjacency matrix has \(n \times n\)  elements. For large-scale supply chains with \(10^4\)  to \(10^5\)  items, the storage of the matrices can take up a lot of memory space and the matrix operations also need significant amount of computational power. Nevertheless, according to our observations of practical large-scale supply chains, the adjacency matrix is typically very sparse. In fact, sparsity is a common feature of large-scale complex networks in the real world [1]}, [2]}. Therefore, we use sparse matrices to represent the adjacency matrices to save memory space as well as to improve the computation efficiency.
